An analog signal is continuous in time, and it can often be necessary to convert the analog signal to a flow of digital values (i.e, a digital signal), which can typically be further processed more easily than the original analog signal. An analog to digital converter (ADC) can be used to accomplish this conversion. An ADC can operate by sampling the value of the input at discrete intervals in time. Provided that the input is sampled at a rate above the Nyquist rate (defined as twice the highest frequency component of the signal), then the digital signal is an accurate representation of the analog signal, and the analog signal can be reconstructed from the digital signal.
However, if the signal is sampled at a rate less than the Nyquist rate, the signal can be incorrectly converted to a signal that is not really representative of the original analog signal. This is commonly referred to as aliasing. Aliasing can occur because instantaneously sampling a function at two or fewer times per cycle can result in missed cycles, and therefore the appearance of an incorrect lower converted frequency. For example, a 2 kHz sine wave being sampled at 1.5 kHz could be reconstructed as a 500 Hz sine wave. It is therefore important to define the rate at which new digital values can be sampled from the analog signal. The rate at which new values are sampled can be called the sampling rate or sampling frequency of the converter.
Bandpass sampling is a widely used approach to sample a continuous-time bandpass signal, and in so doing, downconvert the signal to a lower intermediate frequency (IF). When used in software-defined radios (SDR), bandpass sampling can allow the ADC to be placed closer to the antenna and can eliminate the need for certain analog circuitry components such as mixers, along with their associated nonlinear characteristics. To take advantage of these attributes, however, an appropriate designed IF and sampling frequency must be selected.
Selecting the “right” sampling frequency (FS) and intermediate frequency (IF or fIF) can be hard to do, because to date, only a nonlinear relationship between the intermediate frequency (IF) and sampling frequency (or rate) has been presented when bandpass sampling is used. Cognitive radios (CR) and SDR's have the ability to vary the sampling rate used by their ADC, which changes the IF; but due to the nonlinearity of the aforementioned relationship, it can be challenging (and computationally intensive) to first choose a desired IF and then select the corresponding sampling rate without delving into an iterative, inefficient process.
In view of the above, it is an object of the present invention to provide a bandpass sampling method and device employing such design methods, which use a linear relationship between sampling frequency and IF. Another object of the present invention is to provide a bandpass sampling method and devices that can be used in place of the previously known nonlinear one, and which can find a sampling frequency without iteration in applications where the IF is important. Still another object of the present invention is to provide a bandpass sampling method and device wherein IF is chosen first as the primary design parameter and sampling is then chosen in a deterministic manner, without iteration. Yet another object of the present invention is to provide a bandpass sampling method and devices, which can reduce the complexity of the receiver. Another object of the present invention is to provide a bandpass sampling method and devices, which allow for more efficient allocation of bandwidth resources when multiple signals are being bandpass sampled. Yet another object of the present invention is to provide a bandpass sampling method and devices, which allows for more efficient carrier aggregation. Still another object of the present invention to provide a bandpass sampling method and devices, which can be easy to implement and deploy in a cost-efficient manner.